You should at least remove the excess if you've gotten a sort of gloopy/lumpy surface. This can be done quite effectively by a version of "spiriting off" where you wipe with a pad dampened in alcohol. With care you can remove excess shellac without revealing bare wood in spots and along edges.
If you need to get all the way back to bare wood you can wipe it away with paper towels or a cloth soaked in DA at any stage in the drying process from still sticky to fully hardened, or scrape it off or sand it off as you prefer.
With sanding you need to wait until the shellac has hardened sufficiently so that it doesn't gum up the paper (how long is needed is entirely dependent on the temperature and humidity at your location). It's often best to wait the same amount of time if scraping but not absolutely necessary since you can't clog a scraper in the same way!
start fresh with a cut up t-shirt ...
I'm a big fan of wiping on shellac on small items (not so much for larger stuff) so I think you should at least try it once or twice to see how you get on. If you're deft and fast you can get away with just wiping on with some shellac soaked into a pad of cloth or paper, but to work the shellac into the surface and build a more uniform coat you need to adopt a more full-on French polishing technique and lubricate the pad's surface with a drop or two of oil.
Traditionally the oil used was raw linseed oil but actually the type of oil doesn't really matter as it doesn't become a part of the finish, and many today use mineral oil instead. The oil eventually is removed from the surface by wiping/buffing or during spiriting off.
Re. spiriting off, I wish I could point you to a definitive source but actually I've found there are numerous variations, even among pros. Any decent guide to French polishing, including just a chapter in a wider book on finishing, should include a description of one version of it. Given the authority of the writers presenting the variations I have to assume that all of them do the job and minor differences may simply be a matter of personal preference.